The mass flowmeters belonging to a category commonly known as Cariolis force flowmeter or the convective inertia force flowmeter determine the mass flow rate of media moving through a vibrating conduit by measuring the fluid dynamic reaction (convective inertia force) of the moving fluid to the flexural vibration of the conduit. It is well known fact that the magnitude of the fluid dynamic reaction of the moving fluid to the flexural vibration of the conduit is proportional to the mass flow rate times the gradient of the amplitude of the flexural vibration in the lengthwise direction of the conduit. In order to acquire a good sensitivity with the vibrating conduit mass flowmeter, the flexural vibration of the conduit employed in the mass flowmeter must experience a significant change in the curvature of the conduit during vibration. In other words, a straight conduit employed in the mass flowmeter must bend significantly back and forth during the vibration, and a curved tube must produce a new curvature during the vibration. The present day vibrating conduit mass flowmeters employing a straight vibrating conduit suffer badly from poor sensitivity with few exceptions. Without any exception, the curved conduits employed in the existing vibrating mass flowmeters are vibrated in directions perpendicular to the plane of curvature. As a consequence, none of the existing vibrating conduit mass flowmeters utilizes the advantage provided by the high gradient of the flexural vibration of the fluid moving through a looped conduit resulting from a flexural vibration of the conduit in directions parallel to a plane including the looped conduit.